I Will Give Medal.
Part A: Write the expression x^2 + 7x + 12 as a product of two linear expressions. Show your work and justify each step.

Part B: Rewrite x^2 + 4x + 4 as a square of a linear expression.

Part C: Do the expressions in parts A and B have a common factor? Justify your answer.

Question

I Will Give Medal. 
Part A: Write the expression x^2 + 7x + 12 as a product of two linear expressions. Show your work and justify each step. 
 
Part B: Rewrite x^2 + 4x + 4 as a square of a linear expression.

Part C: Do the expressions in parts A and B have a common factor? Justify your answer.

anonymous · Answer

since $4\times 3=12$ and $4+3=7$ the first one factors as 
$$(x+3)(x+4)$$

anonymous · Answer

$$x^2+4x+4$$ is a perfect square
it is the square of $x+2$ which is another way of saying 
$$x^2+4x+4=(x+2)^2$$

anonymous · Answer

doesn't look like they have any common factors to me, since 
$$(x+3)(x+4)$$ and $$(x+2)(x+2)$$ have no factors that are the same